## Computing NEER, REER and TWI

Posted by Vitalie Ciubotaru

## Notation conventions

$I_{it}$ denotes the amount of imports from country i in period t.
$I_{t}$ denotes total imports of the home country in period t. Strictly speaking, we don’t need total imports to compute the weights, but it is good to know the combined weight of the selected countries in the total (computing the shares of all trading partners is usually infeasible).

## Definitions

### Nominal EER

Nominal Effective Exchange Rate shows the average value of domestic currency against a pool of foreign currencies. A value higher than 1 means nominal appreciation of domestic currency.

$\displaystyle{NEER_t = \prod_{i} (\frac {E_{i0}} {E_{it}})^{w_i}}$
where:
$E_{it}$ denotes the bilateral exchange rate of country i‘s currency in period t (direct quotation — units of domestic currency per unit of foreign currency).
$w_{i}$ denotes the weight of country i and it’s currency in the index. Weights should sum up to unity.

Comment: We could lend more elegance to our formula if we use indirect quotation.

### Real EER

Real Effective Exchange Rate shows the inflation-adjusted average value of domestic currency against a pool of foreign currencies. A value higher than 1 means real appreciation (i.e. an increase in the purchasing power) of domestic currency.

$REER_t = NEER_t \cdot \frac {\displaystyle{P_t}} {\displaystyle{\sum_{i} (w_i P_{it})}}$
where:
$P_{t}$ denotes the home country’s price index in period t.
$P_{it}$ denotes the price index of country i in period t.

$TWI_t = \displaystyle{\prod_{i}} E_{it}^{w_i} \cdot \displaystyle{\sum_{i}}(w_i P_{it})$
$TWI_t = \displaystyle{ \frac { \prod_{i} E_{i0}^{w_i}} {NEER_t} } \cdot \displaystyle{\sum_{i}}(w_i P_{it})$
$TWI_t = \displaystyle{ \frac { \prod_{i} E_{i0}^{w_i}} {REER_t} } \cdot P_t$